Polarization Patterns of Pi 2 Magnetic Pulsations and the Substorm Current Wedge

The results of an analysis of 16 Pi 2 pulsations observed with an extended east-west chain of midlatitude, ground-based magnetometers are reported. The events were chosen such that the center of the substorm current system, defined by using the midlatitude bays associated with these pulsations, was within the longitudinal extent of the station chain. A current wedge model is also used to interpret the observed polarization pattern of the Pi 2 pulsations. This pattern is used to locate the center of the Pi 2 current system. The centers of the Pi 2 and substorm current systems occur at the same meridian for only -65% of the events. This result suggests that the Pi 2 current system and the substorm current wedge are not always the same. The longitudinal extent of the Pi 2 current system estimated from the Pi 2 polarization pattern averages --•90 ø or -6 hours local time for the events in the study. The sense of ellipticity of the waves, anticlockwise looking down the field line in the northern hemisphere, agrees with previous results from these latitudes. Estimates of the wave-phase difference between stations show that, in general, the eastern station of a station pair leads the western one at all local times for both H and D components. When plotted in a substorm coordinate system based on the mid-latitude bay, the phase difference per degree of longitude shows a tendency to decrease in the eastern portion of the current wedge. This longitudinal pattern of phase difference is consistent with the eastern, downward, field-aligned currents being less localized than the western, upward, field-aligned currents.

ization pattern should exhibit a predictable longitudinal pattern.The predicted polarization pattern provides another technique for locating the center of the wedge [Knecht, 1981].Comparing the two techniques, we find that the methods agree in only approximately two thirds of the cases.Little previous work has made use of the substorm current wedge to order the Pi 2 polarization [Knecht, 1981;Samson and Harrold, 1983], although in the past, several apparent local time variations have been reported [Bjornsson et al., 1971;Fukunishi, 1975;Baranskiy et al., 1980;Stuart and Baranskiy, 1982].
The phase differences between stations for Pi 2 pulsations are examined.Although there have been some differences in the results of previous studies [Herron, 1966; Mier-Jedrzejowicz and Southwood, 1979; Baranskiy et al., 1980], the predominant observation is that eastern stations lead in phase.This result has been interpreted as western phase propagation on the entire nightside.Since no physical interpretation consistent with substorm models has been developed, we concluded that a further study of phase variations was warranted.Our results confirm that eastern stations lead in phase, but that the phase variation is not uniform across the substorm current wedge.
The following section describes the magnetometer array and data set used.We then describe the model of the substorm current wedge and the associated, predicted Pi 2 polarization pattern.Examples of Pi 2 pulsations, their polarization pattern, and the related bay structure are then given.The polarization pattern is described for 16 events where it is possible to locate the center of the substorm current system between the two extreme meridians of the network.Finally our results are discussed in the context of previous studies and the three-dimensional current system model.

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The source of data for the study is the AFGL magnetometer network [Knecht et al., 1979].The geographic and corrected geomagnetic coordinates of the seven AFGL stations are given in Table 1.Five of these stations are at --•55 ø corrected geomagnetic latitude, and the remaining two stations are at --•40 ø (Figure 1).The latitudes of the stations place them all on field lines which thread the plasmasphere, although it is possible that during extremely disturbed magnetic conditions the plasmapause may move far enough radially inward to place the field lines of the northern stations in the plasma trough.Data from the two southern with occasional differences between studies being reported.
Since Pi 2 pulsations are associated with substorms, it seems natural to use the position of the stations relative to some substorm feature to better organize the data.Features such as the auroral breakup region [Kuwashima and $aito, 1981] or the auroral electrojet [Rostoker and Samson, 1981; Samson and Rostoker, 1983] would be useful, but no method of reliably locating them with mid-latitude data is available.Figure 3 shows schematically the field-aligned and ionospheric legs of the substorm current wedge and the magnetic variations caused by the two field-aligned currents.The field-aligned currents will, ideally, only affect the horizontal magnetic components at mid-latitudes.If the Pi 2 pulsation is directly associated with the substorm current system, then it will have the predicted polarization pattern across the current wedge shown in Figure 3.This pattern can be tested by using events where the center of the current wedge, located by the bay current system, is between the two longitudinal extremes of the magnetometer chain.
In order to quantify the bay structure for each Pi 2 event  4), the hodogram at NEW, the station with the smallest wave amplitude, does not fit the predicted pattern inside the current wedge (Figure 3).However, it is consistent with the pattern predicted to the west of the western field-aligned current part of the wedge (not shown in Figure 3).At the other stations the polarization pattern is similar to the predicted one and points to a location between MCL and SUB.There is also some time variation of the azimuth at SUB, but the average azimuth fits the predicted pattern.For the later event, shown in Figure 5, the predicted pattern of the azimuth (Figure 3 In the substorm current wedge model (Figure 3) the position where the azimuth of the magnetic perturbation is directed east-west locates the longitudes of the field-aligned current parts of the wedge.The difference in longitude between the field-aligned current portions can be regarded as the effective width of the wedge.Since it is unusual for the entire width of the wedge to be located within the two longitudinal extremes of the network, the wedge width was estimated from the slope of the lines connecting the dots or crosses for each individual event.This slope varies from ---1 ø to ---2.5 ø azimuth/degree longitude, with an average of---2 ø azimuth/degree longitude.This implies a variation in the wedge width of between ---4 and ---12 hours and an average of ---6 hours.These results are in reasonable agreement with the observations of Clauer and McPherron [1974b], who found the extent of the current system to vary between 2.5 and 10 hours, with an average of just over 4 hours.
The ellipticity variation with respect to Along is shown in Figure 8, where all but two values are negative.The predominance of anticlockwise values agrees with other results for stations at these latitudes [e.g., Fukinishi, 1975; Mier-Jedrzejowicz and Southwood, 1979; Lester and Orr, 1981].Apart from this, no ordering appears in the sense of polarization with respect to Along.Also, we found no systematic local time variation of ellipticity.

STATIONS
The longitudinal variation of pulsation phase has been discussed in the past in terms of the rn number [e.g., Green, 1976;Mier-Jedrzejowicz and Southwood, 1979].The m number is obtained by dividing the phase difference between a pair of stations by the station longitudinal separation.It has then been interpreted in terms of an apparent azimuthal wave number.However, since the azimuthal propagation of the Pi 2 signal is not clear, we shall not interpret the m number in this way but simply consider it as the phase difference per degree of longitude.The phase differences between all possible pairs of stations were calculated by using a cross-spectral analysis technique [Hughes et al., 1978].Only the phase differences between adjacent station pairs are used here.The 95% confidence limits in the phase difference were calculated by using the coherency value and the number of degrees of freedom associated with the smoothing parameter used in the spectral computation [Green, 1976].We calculated the m number from the calculated phase difference and an error in m, Am, from the confidence limits in the phase difference.
Figure 9 shows the m values for the 11 events where the two methods of identifying the center of the substorm current wedge agree.The error bar, representing Am, is plotted if Am > Iml, i.e., there is ambiguity in the sign of m.
We included only those points for which Am < 1.5.This value was chosen as a compromise between having sufficient number of points and sufficient resolution in m.The maximum error allowed, Am = 1.5, is also shown.The H component (Figure 9a  The occasional disagreement between the center of the wedge identified by the two methods implies that if the Pi 2 pulsation is associated with a three-dimensional current system then that current system is not always colocated with the substorm current system.A study by Pashin et al. [1982] appears to support this result, as they also conclude that the wave and substorm current systems are offset.However, since they were using data from a small region at high latitudes, the exact relationship between their results and ours requires further study.Alternatively, the Pi 2 could be linked to the substorm current system only at onset (J.C. Samson, personal communication, 1982).After onset there often is a westward expansion of the current system, which will affect the bay at mid-latitudes.In this case the center identified by z•D -0 would be to the west of that identified by the Pi 2 polarization pattern.This happens in four out of five of the cases where the two methods disagreed.
As previously mentioned, we believe the wedge current system discussed in this paper is an oversimplification of the real current systems [Baumjohann et al., 1981].There are several situations that could account for discrepancies between observations and model.First, there are likely to be current systems located outside the current wedge.Second, preexisting currents in the vicinity of the substorm current wedge can confuse the bay pattern.Third, the currents may be distributed in both latitude and longitude.Nevertheless, we have demonstrated that the simple wedge model often orders the data well.
In this paper we are not attempting to completely describe the currents that are an integral part of the Pi 2 wave.Since Pi 2 polarizations are generally elliptical, the current patterns must move periodically.What we have found is that the largest magnetic perturbations, those corresponding to the major axes of the polarization ellipses, do fit a current topologically similar to the substorm current system.The magnetic signature seen at one ground station describes the integrated effect of currents flowing in a substantial region of the ionosphere.If the ionosphere conductivity is uniform, the ground signature results from Hall currents alone [Hughes and Southwood, 1976].However, at night the conductivity is far from uniform; the auroral zone can have a substantially higher conductivity than the surrounding ionosphere.In this case the ground signature can only be determined by a full Biot-Savart integration of the ionospheric and field-aligned currents.The inverse problem is inherently nonunique.A full description of the currents associated with a Pi 2 pulsation must await further study.
The predominance of negative m values in both H and D components found in section 6 agrees with Mier-Je-drzeJowicz and Southwood [1979] and Warner [1979] but not Herron [1966].Previously, m values have been interpreted as plane-wave wave numbers, which in this case implies westward phase propagation across the entire nightside.We consider it dangerous to interpret m values in this way.To do so implies a Pi 2 wave source on the morningside of the magnetosphere, and we have seen no substorm model that can incorporate this interpretation, since substorms are a nightside phenomenon with a peak occurrence between 22 LT and local midnight.
Finally, the weak tendency of Iml to decrease to the east of the center of the wedge is consistent with the eastern field-aligned currents being located over a wider longitudinal range than the more intense upward field-aligned currents at the western part of the current system.This result is , suggested by the tendency for localized structures to be associated with higher m numbers.Such a current system has been implied from ground-based magnetometer measurements and STARE electric field measurements in Scandinavia [Baumjohann et al., 1981].Westward motion of such a current system relative to the ground observations would mean that the phase change would be larger at the western part of the array, and the eastern stations would lead in phase.Such motion of the substorm current system does seem to occur [e.g., Wiens and Rostoker, 1975].

SUMMARY AND CONCLUSIONS
Results from a study of Pi 2 pulsations observed on an east-west chain of magnetometers have been presented.We have concentrated on the relationship between magnetic bays and Pi 2 polarization characteristics.We also calculated the phase differences between adjacent station pairs.We can summarize the results as follows: 1.The magnetic bays observed at mid-latitude ground stations can be used to locate the center of the substorm current wedge.
2. A predicted Pi 2 polarization pattern based on a current wedge model is observed in each of 16 events.
3. Two methods for locating the center of the substorm current wedge agreed in 11 out of 16 cases.
4. Using the Pi 2 azimuths, the effective width of the Pi 2 current system was estimated to have an average value of 6 hours for the 16 events.5.There is no systematic variation in ellipticity with either local time or the substorm current system.
6. Wave phase differences between stations, or m, are predominantly negative in both H and D components.
7. Wave phase difference between stations tends to decrease to the east of the center of the substorm current wedge, consistent with western upward field-aligned currents being more localized than the eastern downward currents.
The simple three-dimensional substorm current wedge model orders Pi 2 polarization data well.The relationship between the Pi 2 polarization and the substorm bay shows that the two current systems are not always colocated.This is important both in terms of the generation mechanism of the Pi 2 pulsation and also in gross substorm dynamics.Further study of this property will be carried out, and it is hoped that the results will provide more information on the processes involved in the generation of Pi 2 pulsations and their relationship with substorm onset.

Fig. 1 .
Fig. 1.Map showing the locations of the AFGL network stations.The five northern stations, extending over 4 hours local time, are at ---55 ø corrected geomagnetic latitude' the two southern stations, which are not used in this study, are at ---40 ø .
by using the location of the wedge relative to a station has clear advantages over the use of local time.The simple current system discussed by McPherron et al. [1973] and developed further by Clauer and McPherron [ 1974a] is used as the model and is shown in Figure 2. At the onset of the expansion phase of the substorm the crosstail current is diverted down the magnetic field lines.Current then flows in the ionosphere as the westward electrojet and returns to the tail along the magnetic field lines.The perturbation tail current can be represented by an equivalent eastward current, which completes the three-dimensional current wedge.Although this current system is an oversimplification several authors [e.g., McPherron et al., 1973;

Fig. 2 .
Fig. 2. The upper panel shows schematically the model of the substorm current wedge which is used to position the stations relative to the center of the substorm wedge.The bottom panel (right) shows an equivalent current system and model parameters.The bottom panel (left) summarizes the calculated sense and magnitude of the mid-latitude magnetic bay expected after substorm onset [from Clauer and McPherron, 1974a].Clauer and McPherron, 1974a] have shown that it accurately describes mid-latitude bay variations.The mid-latitude signature of this wedge is a positive perturbation in the northsouth magnetic component symmetric about the central meridian of the current system and a perturbation in the eastwest magnetic component that is positive to the west and negative to the east of the central meridian.
Fig. 3.A schematic view of the ionospheric and field-aligned portions of the substorm current wedge model shown in Figure 2. Also shown are the predicted Pi 2 polarization azimuths at mid-latitudes within the two extreme meridians of the current system if the Pi 2 is a result of the oscillation of such a current system.

Fig. 6 .Fig. 7 .
Fig 5. Same as Figure 4 for a Pi 2 pulsation in the interval 0555-0610 UT on March 14, 1978.When no arrow is present the ellipticity is essentially linear.The hodograms between 0559-0603 UT from all five stations compare .
) shows a weak tendency for Iml to decrease from west to east across the wedge.The D component (Figure 9b) shows a similar tendency for the values to the east of the center to decrease with increasing Along.The larger Iml values are west of center of the wedge for the H component and close to the center for the D component.The m values are predominantly negative, irrespective of the location of the center of the substorm current wedge and local time (results not presented).This agrees with the work of Mier-Jedrzejowicz and Southwood [ 1979], Warner [1979], and Green and Stuart [1979].Mier-Jedrzejowicz and Southwood did not use individual events, but power levels in the Pi 2 frequency band averaged over 1 hour time intervals.Warner, however, studied individual Pi 2 events observed with the same network as Mier-Jedrzejowicz and Southwood.Baranskiy et al. [1980] reported that there was a slight tendency for m to change sign near midnight.They have shown the H component of the western station leading before midnight and the D component of the western station leading after midnight.Neither reversal is seen in our results.Also, there is no sign of the reversal reported pattern was better organized by the substorm current wedge and not by local time.Measurements made by Green and Stuart [1979; personal communication, 1980] and Baranskiy et al. [1980] support our results.Two examples of the azimuth of the major axis of the polarization ellipse [see Figure 5, Baranskiy et al., 1980] illustrate the pattern predicted by a current wedge model.Furthermore, using many events, Baranskiy et al. did not find a systematic variation with local time (see their Figure

Fig. 9 .
Fig. 9.The phase difference per degree of longitude, rn value, between pairs of stations plotted against the Along of the midpoints of the two stations for H (9a) and D (9b); rn is calculated by using only adjacent station pairs for the 11 events where the two methods of locating the center of the current system agree.Positive (negative) rn indicates the western (eastern) station leads in phase.Error bars are marked if Am >Im I and the maximum error in any value plotted is 1.5.6c).However, there have been some studies which suggest a local time organization of the Pi 2 polarization pattern [e.g., Bjornsson et at., 1971; Fukinishi, 1975; Stuart and Baranskiy, 1982].Bjornsson et at.[1971], using averages of Pi 2 azimuths determined in 1 hour local time bins at stations between 40 ø and 50 ø magnetic latitude, found a pattern similar to that in Figure 3, but pointing to the 2200 LT meridian.These correlations between Pi 2 azimuths and local time would be expected if the centers of the current systems associated with the pulsations used in a study had a small local time spread.We are unable to test this explanation because the studies showing a local time organization of the Pi 2 azimuths do not indicate the location of the wedge centers.In this paper the centers of the current systems were found to range from 1940 to 0100 LT, a range that makes it